The Getty is a huge (free) museum in LA. It houses everything from modern photos to antique European furniture (although the gardens are my personal favorite). But I'm actually a bigger fan of the Getty Villa. Nestled in Malibu, it feels like a hidden gem overlooking the coast. It's much more specialized: focusing on Roman and Greek art and architecture.
It's someplace I can definitely see myself sipping a cup of coffee and lingering over the different art pieces. Just looking at these pictures inspires me to add a little romanticism into my style.